Self-interference incoherent digital holography (SIDH) retrieves the object information from the digital hologram illuminated by the incoherent light. However, the reconstructed image according to different sections will be disturbed by the out-of-focus sectional image by employing the traditional numerical reconstruction method. Therefore, a numerical reconstruction method for SIDH by employing compressive sensing (CS) is proposed to achieve the reconstruction of three-dimensional (3D) sectional image.Firstly, according to CS, the sensing operator is built up based on the physical mechanism of SIDH. And then,the recovery algorithm is employed for the image restoration. Numerical simulation and experimental research on SIDH employing several LEDs at different positions are performed to demonstrate the feasibility and validity of the method. In addition, the relationship of the reconstructed distance according to different sectional images and the experimental parameters is discussed. The analysis result shows that different sectional images can be reconstructed with the out-of-focus section information inhibited.